Freediving world champion Natalia Molchanova was giving a diving lesson to several inexperienced divers when she failed to surface, it has emerged.

Molchanova, 53, vanished on Sunday as she was freediving – diving without breathing apparatus – near Formentera, a small island south of Ibiza. Initial reports said she was diving without fins to a planned depth of 35 metres, where it was feared she may have encountered a strong underwater current.

But according to her son, Alexey Molchanov, the freediver travelled to the Balearic islands to provide private freediving instruction to Russian property developer Pavel Tyo and at least one other person. The new details, published in the New York Times, contradict earlier sources who said Molchanova had been diving in the area recreationally.

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Local media reports said Tyo, a co-owner of Moscow’s Capital Group, owns a home in Ibiza. On Sunday, he and several others sailed to nearby Formentera in Tyo’s superyacht Pumpkin. The yacht docked at the La Savina port and made their way some two miles out to sea.

Molchanova would have dropped a 20-metre line, a standard length for beginning freedivers, and it is likely the students would have taken turns to descend, gently increasing the depth of their descent with each dive, said her son.

Molchanova would have accompanied her students on each dive. Alexey Molchanov said his mother also freedived on her own to unknown depths several times between instructional dives.

The reports suggest that Molchanova would have been the only experienced freediver in the water. Speaking to the Guardian earlier this week, Kimmo Lahtinen of the freediving governing body AIDA, underscored the importance of freedivers being accompanied by a capable safety diver. “Never do it alone,” he said.

On Sunday, when Molchanova failed to surface, the crew of the Pumpkin radioed Spain’s coastguard and deployed additional boats in an attempt to locate her. A helicopter soon joined the search, monitoring the area overhead, while coastguard authorities combed the area for any sign of the freediver.

In the following days the search went underwater, with a robot brought in to widen the search and work alongside a special team of divers from the Guardia Civil.

On Wednesday Spanish rescue services called off the underwater search for Molchanova. The Guardia Civil said it plans to continue a surface search for the freediver until Sunday.

Molchanova was diving in an area known for strong currents and heavy boat traffic, where the water temperature can dip sharply once divers get below the surface – something that can affect even the most experienced of divers.

Widely considered to be the greatest freediver of all time, Molchanova holds 41 world records in freediving and can hold her breath for nine minutes. In May, she dived to a depth of 71 metres in waters off Egypt.

In 2013, Molchanova swam 182 metres underwater with no fins at the world championships in Belgrade, breaking the record by 19 metres.

At the following year’s world championship in Sardinia she broke the world record with a fin by swimming for 237 metres. In total she has won 20 world championship individual golds.